JNTU
JNTU B.Tech III Year DYNAMICS OF MACHINERY Previous Question Paper (February - 2023 - R16)
Note: i) Question paper consists of Part A, Part B. ii) Part A is compulsory, which carries 25 marks. In Part A, Answer all questions. iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.
Part A
In static force analysis, are the inertia forces considered along with static forces? Give reason for the answer.
Answer
No, inertia forces are not considered in static force analysis. Static force analysis assumes that the mechanism is in a state of equilibrium under the action of external forces and torques, implying that the acceleration of all moving parts is zero. Inertia forces, which are defined by the product of mass and acceleration (F = ma), only arise when there is motion with acceleration, which is the domain of dynamic force analysis.
What are the pitch, roll, and yaw motions of ship? Explain briefly.
Answer
The motions of a ship are defined relative to its center of gravity and three mutually perpendicular axes. These angular motions are essential in the study of ship stability and gyroscopic effects:
- Pitch: This is the angular motion of the ship about the transverse axis (side-to-side). It involves the bow and stern moving alternately up and down, typically caused by waves striking the ship from the front or rear.
- Roll: This is the angular motion of the ship about the longitudinal axis (front-to-back). It involves the ship oscillating from side to side, often caused by waves hitting the beam (side) of the ship.
- Yaw: This is the angular motion of the ship about the vertical axis. It represents the deviation of the ship's bow from its intended course, effectively causing the ship to swing left or right as it travels forward.
What are crank effort diagrams? What is their use?
Answer
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In a reciprocating engine, the tangential force acting on the engine is 150 kN and crank radius is 300 mm. What is the torque acting on the crank?
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Which parameters can be measured using a dynamometer?
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“Frictional torque transmitted by uniform wear theory is more than torque transmitted by uniform pressure theory” – True or false? Give reason for the answer.
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Define the stability of governor.
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Why is only a part of the unbalanced force due to reciprocating masses balanced by revolving mass? Why complete balancing is not possible in reciprocating engine?
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Define node in torsional vibration.
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A cantilever shaft having 50 mm diameter and a length of 300 mm has a disc of mass 100 kg at its free end. The Young’s modulus for the shaft material is 200 GN/m2. What is the frequency of transverse vibrations of the shaft?
Answer
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Part B
Derive an expression for gyroscopic torque in terms of the angular velocity of spin, angular velocity of precession, and polar mass moment of inertia of a disc.
Answer
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What is Shaking Force? How is it determined for a Four – Bar mechanism?
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In a four-bar mechanism, the link dimensions are AB = 30 cm, BC = 30.5 cm, AD = 56 cm, CD = 30 cm. The link AB makes an angle 45° with the horizontal. A horizontal force ‘P’ (1500 N) is acting on link CD at 10 cm from D. Find the torque applied at link AB to keep the mechanism in static equilibrium.
Answer
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When and why is the correction coupled applied while considering the inertia of the connecting rod of a reciprocating engine?
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A single cylinder engine is producing 25 HP at 4000 rpm with 2000 explosions per minute. The fluctuation of speed is not to exceed 1% on either side. Find the dimensions of a solid flywheel so that the hoop stress does not exceed 10 MPa. Assume that the work done during the power stroke is 1.4 times work done during the cycle. Density of flywheel material is 7200kg/m3.
Answer
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A three cylinder single acting engine has its cranks set equally at 120° and it runs at 600 r.p.m. The torque-crank angle diagram for each cycle is a triangle for the power stroke with a maximum torque of 90 N-m at 60° from dead center of corresponding crank. The torque on the return stroke is sensibly zero. Determine the:
- Power developed.
- Coefficient of fluctuation of speed, if the mass of the flywheel is 12 kg and has a radius of gyration of 80 mm.
- Coefficient of fluctuation of energy.
- Maximum angular acceleration of the flywheel.
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Describe, with a sketch, the working of a single plate friction clutch.
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In a band brake, the band is wrapped on the 3/4th of circumference of the brake drum. The diameter of the brake drum is 500 mm. The band brake provides a braking torque of 355 Nm. One end of the band is attached to a fulcrum pin of the lever and the other end to a pin 150 mm from the fulcrum. A force is applied on the lever at a distance of 600 mm from the fulcrum, and the coefficient of friction is 0.35. Find the force applied on the end of the lever when the drum rotates in the anticlockwise direction.
Answer
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Explain the concepts of ‘Friction Circle’ and ‘Friction Axis’ with the help of suitable diagrams.
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Calculate the torque transmitted by a clutch having four shoes, which has a spring force of 700 N and centrifugal force of 4000 N. Rim diameter is 560 mm and coefficient of friction is 0.3.
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Explain the terms: variation of tractive force; swaying couple and hammer blow.
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Calculate the minimum speed of a Proell governor, which has equal arms each of 200 mm and are pivoted on the axis of rotation. The mass of each ball is 4 kg and the central mass on the sleeve is 20 kg. The extension arms of the lower links are each 60 mm long and parallel to the axis when the minimum radius of the ball is 100mm.
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Each crank and connecting rod of a four crank in-line engine are 200 mm and 800 mm respectively. The outer cranks are set at 120° to each other and each has a reciprocating mass of 200 kg. The placing between adjacent planes of cranks are 400 mm, 600 mm and 500 mm. If the engine is in complete primary balance, determine the reciprocating masses of the inner cranks and their relative angular positions. Also find the secondary unbalanced force if the engine speed is 210 rpm.
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Derive the expression for the natural frequency of free torsional vibrations of two – rotor system.
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A spring mass system has spring stiffness ‘s’ N/m and has a mass of ‘m’ kg. It has a natural frequency of vibration as 12 Hz. An extra 2 kg mass is coupled to ‘m’ and the natural frequency reduces by 2 Hz. Find the value of ‘s’ and ‘m’.
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When does the Whirling of Shafts occur? Explain with a sketch. If the speed of operation of a machine shaft is above the whirling speed, how is this problem of passing over the whirling speed taken care of?
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Find the frequency of transverse vibrations of a shaft which is simply supported at the ends and is of 40 mm in diameter. The length of the shaft is 5 m. The shaft carries three point loads of masses 15 kg, 35 kg and 22.5 kg at 1 m, 2 m and 3.4 m respectively from the left support. The Young’s modulus for the material of the shaft is 200 GN/m2. The weight of the shaft is 18.394 N per meter length.
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